The present invention provides a preparation process for converting to a vinylidene fluoride elastomer having a group having sulfinic acid, sulfinic acid derivative, sulfonic acid or sulfonic acid derivative at one end or both ends of its trunk chain, and the preparation process provides a vinylidene fluoride elastomer having, at one end or both ends of its trunk chain, end groups represented by the formula: —CR1R2—CR3R4—SO2H, wherein R1 to R4 may be the same or different and each is hydrogen atom or fluorine atom, by allowing a vinylidene fluoride elastomer having, at one end or both ends of its trunk chain, end groups represented by the formula: —CR1R2—CR3R4—X1, wherein R1 to R4 are as defined above, X1 is bromine atom or iodine atom, to react with a sulfur compound represented by the formula: (M1)nH2-nS2O4, wherein M1 is a monovalent or divalent metal ion or ammonium ion, n is an integer of 0 to 2.